![]() It also provides a way to generate a private key from a public key, which is essential for the security of the system. ![]() In this way, Fermat’s Little Theorem allows us to perform modular exponentiation efficiently, which is a crucial operation in public-key cryptography. To decrypt the message, the recipient simply computes m = c b m o d n m = c^b \bmod n m = c b mod n, which (by Fermat’s Little Theorem) is equivalent to m = ( m a ) b m o d n = m ( a b ) m o d n = m 1 m o d n = m m o d n m = (m^a)^b \bmod n = m^(ab) \bmod n = m^1 \bmod n = m \bmod n m = ( m a ) b mod n = m ( ab ) mod n = m 1 mod n = m mod n. To encrypt a message with the user’s public key ( n, a ) (n, a) ( n, a ), we first convert the message into a number m m m (using some agreed-upon scheme), and then compute the encrypted message c c c as c = m a m o d n c = m^a \bmod n c = m a mod n. This means that when we multiply a a a and b b b together, the result is congruent to 1 1 1 modulo n n n. The user’s private key would be the pair ( n, b ) (n, b) ( n, b ), where b b b is the modular multiplicative inverse of a modulo n n n. The user’s public key would then be the pair ( n, a ) (n, a) ( n, a ), where aa is any integer not divisible by p p p or q q q. ![]() We might choose two large prime numbers, p p p and q q q, and then compute the product n = p q n = pq n = pq. For example, suppose we want to generate a public-key cryptography system for a user with the initials “ABC”. One way to generate these keys is to use prime numbers and Fermat’s Little Theorem. In a public-key cryptography system, each user has a pair of keys: a public key, which is widely known and can be used by anyone to encrypt a message intended for that user, and a private key, which is known only to the user and is used to decrypt messages that have been encrypted with the corresponding public key. One of the most common applications is in the generation of so-called “public-key” cryptography systems, which are used to securely transmit messages over the internet and other networks. How may I help you? (exit USCIS to YouTube).Fermat’s Little Theorem is used in cryptography in several ways. To learn more about Emma and see examples of questions applicants are asking her, check out this short video: Hello, I'm Emma. To send your feedback or ask for technical support, please email us at Please do not send questions about your personal situation or case to this mailbox instead, check your case status online or call us at 80. Emma works on desktop and laptop computers and mobile devices.Įmma’s development team is continuously refining her knowledge base to improve your experience. Getting Emma’s help is easy: just click the “Need Help? Ask Emma” link in the upper right corner of the page or the “Need Help” icon on the bottom of some pages. (Currently, the sound feature is only available on our English website.) Chatting with Emma is Easy If you have the sound on, she’ll also talk to you. Below Emma’s answer, she might also offer information related to your question. Find information based on the questions and search terms you use.Įmma is fluent in both English and Spanish, and she will always type out her answers.Provide immediate responses to your questions about all of our services.She also knows a lot of common search terms. What Can Emma Do?Įmma answers questions based on your own words you don't need to know “government speak”. Inspired by her namesake, our Emma can help you find the immigration information you need. Emma is named for Emma Lazarus, who wrote the poem inscribed at the base of the Statue of Liberty about helping immigrants. Meet “Emma,” a computer-generated virtual assistant who can answer your questions and even take you to the right spot on our website.
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